Right lines
(A C
and
B D)
which join the adjacent extremities of two equal and
parallel right lines
(A B
and
C D)
are themselves equal and parallel.

Draw the diagonal
A D,
and in the triangles
C D A
and
B A D
the sides
C D
and
B A
are equal (by hyp);
ABCDA D
is common to both triangles, and the angle
C D A
is equal to the alternate
B A D(XXIX);
therefore the lines
A C
and
B D
are equal, and also the angles
C A D
and
B D A;
therefore the right line
A D
cutting the right lines
A C
and
B D
makes the alternate angles equal, and therefore
(XXVII)
the right lines
A C
and
B D
are parallel.